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The algebra of smooth functions of rapid descent
(2009)
A bounded operator with the spectrum lying in a compact set V ⊂ R, has C∞ (V) functional calculus. On the other hand, an operator H acting on a Hilbert space H, admits a C(R) functional calculus if H is self-adjoint. So ...
Operators with slowly growing resolvents towards the spectrum
(Academic Publications, 1/13/2009)
A closed densely defined operator H, on a Banach space X, whose spectrum is contained in R and satisfies
(z −H)−1
≤ c hziα |=z|β ∀ z 6∈ R (0.1) for some α , β ≥ 0; c > 0, is said to be of (α, β)−type R . If instead of (0.1) ...
The algebra of smooth functions of rapid descent
(2009)
A bounded operator with the spectrum lying in a compact set V ⊂
R, has C∞(V ) functional calculus. On the other hand, an operator H acting on
a Hilbert space H, admits a C(R) functional calculus if H is self-adjoint. So ...